首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 832 毫秒
1.
Finite-frequency sensitivity kernels for head waves   总被引：2，自引：0，他引：2  
Head waves are extremely important in determining the structure of the predominantly layered Earth. While several recent studies have shown the diffractive nature and the 3-D Fréchet kernels of finite-frequency turning waves, analogues of head waves in a continuous velocity structure, the finite-frequency effects and sensitivity kernels of head waves are yet to be carefully examined. We present the results of a numerical study focusing on the finite-frequency effects of head waves. Our model has a low-velocity layer over a high-velocity half-space and a cylindrical-shaped velocity perturbation placed beneath the interface at different locations. A 3-D finite-difference method is used to calculate synthetic waveforms. Traveltime and amplitude anomalies are measured by the cross-correlation of synthetic seismograms from models with and without the velocity perturbation and are compared to the 3-D sensitivity kernels constructed from full waveform simulations. The results show that the head wave arrival-time and amplitude are influenced by the velocity structure surrounding the ray path in a pattern that is consistent with the Fresnel zones. Unlike the 'banana–doughnut' traveltime sensitivity kernels of turning waves, the traveltime sensitivity of the head wave along the ray path below the interface is weak, but non-zero. Below the ray path, the traveltime sensitivity reaches the maximum (absolute value) at a depth that depends on the wavelength and propagation distance. The sensitivity kernels vary with the vertical velocity gradient in the lower layer, but the variation is relatively small at short propagation distances when the vertical velocity gradient is within the range of the commonly accepted values. Finally, the depression or shoaling of the interface results in increased or decreased sensitivities, respectively, beneath the interface topography.  相似文献   

2.
It is now widely accepted that elastic properties of the continental lithosphere and the underlying sublithospheric mantle are both anisotropic and laterally heterogeneous at a range of scales. To fully exploit modern three-component broad-band array data sets requires the use of comprehensive modelling tools. In this work, we investigate the use of a wide-angle, one-way wave equation to model variations in teleseismic 3-D waveforms due to 2-D elastic heterogeneity and anisotropy. The one-way operators are derived based on a high-frequency approximation of the square-root operator and include the effects of wave propagation as well as multiple scattering. Computational cost is reduced through a number of physically motivated approximations. We present synthetic results from simple 1-D (layer over a half-space) and 2-D (subduction zone) models that are compared with reference solutions. The algorithm is then used to model data from an array of broad-band seismograph stations deployed in northwestern Canada as part of the IRIS-PASSCAL/LITHOPROBE CANOE experiment. In this region radial-component receiver functions show a clear continental Moho and the presence of crustal material dipping into the mantle at the suture of two Palaeo-Proterozoic terranes. The geometry of the suture is better defined on the transverse component where subduction is associated with a ∼10 km thick layer exhibiting strong elastic anisotropy. The modelling reproduces the main features of the receiver functions, including the effects of anisotropy, heterogeneity and finite-frequency scattering.  相似文献   

3.
The perfectly matched layer (PML) absorbing boundary condition is incorporated into an irregular-grid elastic-wave modelling scheme, thus resulting in an irregular-grid PML method. We develop the irregular-grid PML method using the local coordinate system based PML splitting equations and integral formulation of the PML equations. The irregular-grid PML method is implemented under a discretization of triangular grid cells, which has the ability to absorb incident waves in arbitrary directions. This allows the PML absorbing layer to be imposed along arbitrary geometrical boundaries. As a result, the computational domain can be constructed with smaller nodes, for instance, to represent the 2-D half-space by a semi-circle rather than a rectangle. By using a smooth artificial boundary, the irregular-grid PML method can also avoid the special treatments to the corners, which lead to complex computer implementations in the conventional PML method. We implement the irregular-grid PML method in both 2-D elastic isotropic and anisotropic media. The numerical simulations of a VTI lamb's problem, wave propagation in an isotropic elastic medium with curved surface and in a TTI medium demonstrate the good behaviour of the irregular-grid PML method.  相似文献   

4.
VSP data collected in the KTB (Germany) borehole to a depth of 8.5 km in 1999 show a surprising spectral modulation of the downgoing wavefield. After filtering the data with the singular value decomposition technique it was found that below about 6.2 km there are two depth intervals where the modulation can be explained in terms of a basic wavelet plus two weighted and delayed copies of that wavelet, with the delay for each wavelet remaining almost constant in each interval. The boundary between the two intervals is at about 7.25 km depth and above and below this depth the delay for the second wavelet is almost the same, while the delay for the third wavelet is significantly different. Neither the modulation nor its depth variation are source related and cannot be explained in terms of multiple reflections in a subhorizontal low-velocity layer. On the other hand, finite difference synthetic data show that subvertical layering (which is prevalent in the borehole area) provides a mechanism that can explain the observations. This mechanism has analogies with the generation of the standard refracted (i.e. head) waves. When a plane wave front propagates perpendicular to the boundaries of a vertical low-velocity layer surrounded by two vertical high-velocity layers, refracted wave fronts are generated in the low-velocity layer, which in turn generate secondary wave fronts in the high-velocity layers. These wave fronts trail the primary wave fronts by a constant delay whose magnitude has a simple dependence on the thickness of the low-velocity layer and the velocities involved. This process creates multipath arrivals that in geological settings with steeply inclined and faulted layers may appear and disappear rather abruptly, which may contribute to a scattered appearance of the wavefield.  相似文献   

5.
Finite difference (FD) simulation of elastic wave propagation is an important tool in geophysical research. As large-scale 3-D simulations are only feasible on supercomputers or clusters, and even then the simulations are limited to long periods compared to the model size, 2-D FD simulations are widespread. Whereas in generally 3-D heterogeneous structures it is not possible to infer the correct amplitude and waveform from 2-D simulations, in 2.5-D heterogeneous structures some inferences are possible. In particular, Vidale & Helmberger developed an approach that simulates 3-D waveforms using 2-D FD experiments only. However, their method requires a special FD source implementation technique that is based on a source definition which is not any longer used in nowadays FD codes. In this paper, we derive a conversion between 2-D and 3-D Green tensors that allows us to simulate 3-D displacement seismograms using 2-D FD simulations and the actual ray path determined in the geometrical optic limit. We give the conversion for a source of a certain seismic moment that is implemented by incrementing the components of the stress tensor.
Therefore, we present a hybrid modelling procedure involving 2-D FD and kinematic ray-tracing techniques. The applicability is demonstrated by numerical experiments of elastic wave propagation for models of different complexity.  相似文献   

6.
Today's numerical methods like the Spectral Element Method (SEM) allow accurate simulation of the whole seismic field in complex 3-D geological media. However, the accuracy of such a method requires physical discontinuities to be matched by mesh interfaces. In many realistic earth models, the design of such a mesh is difficult and quite ineffective in terms of numerical cost. In this paper, we address a limited aspect of this problem: an earth model with a thin shallow layer below the free surface in which the elastic and density properties are different from the rest of the medium and in which rapid vertical variations are allowed. We only consider here smooth lateral variations of the thickness and elastic properties of the shallow layer. In the limit of a shallow layer thickness very small compared to the smallest wavelength of the wavefield, by resorting to a second order matching asymptotic approximation, the thin layer can be replaced by a vertically smooth effective medium without discontinuities together with a specific Dirichlet to Neumann (DtN) surface boundary condition. Such a formulation allows to accurately take into account complex thin shallow structures within the SEM without the classical mesh design and time step constraints. Corrections at receivers and source—when the source is located within the thin shallow layer—have been also derived. Accuracy and efficiency of this formulation are assessed on academic tests. The stability and limitations of this formulation are also discussed.  相似文献   

7.
We have been developing an accurate and efficient numerical scheme, which uses the finite-difference method (FDM) in spherical coordinates, for the computation of global seismic wave propagation through laterally heterogeneous realistic Earth models. In the field of global seismology, traditional axisymmetric modeling has been used widely as an efficient approach since it can solve the 3-D elastodynamic equation in spherical coordinates on a 2-D cross-section of the Earth, assuming structures to be invariant with respect to the axis through the seismic source. However, it has the severe disadvantages that asymmetric structures about the axis cannot be incorporated and the source mechanisms with arbitrary shear dislocation have not been attempted for a long time. Our scheme is based on the framework of axisymmetric modeling but has been extended to treat asymmetric structures, arbitrary moment-tensor point sources, anelastic attenuation, and the Earth center which is a singularity of wave equations in spherical coordinates. All these types of schemes which solve 3-D wavefields on a 2-D model cross-section are classified as 2.5-D modeling, so we have named our scheme the spherical 2.5-D FDM. In this study, we compare synthetic seismograms calculated using our FDM scheme with three-component observed long-period seismograms including data from stations newly installed in Antarctica in conjunction with the International Polar Year (IPY) 2007–2008. Seismic data from inland Antarctica are expected to reveal images of the Earth's deep interior with enhanced resolution because of the high signal-to-noise ratio and wide extent of this region, in addition to the rarity of sampling paths along the rotation axis of the Earth. We calculate synthetic seismograms through the preliminary reference earth model (PREM) including attenuation using a moment-tensor point source for the November 9, 2009 Fiji earthquake. Our results show quite good agreement between synthetic and observed seismograms, which indicates the accuracy of observations in the Antarctica, as well as the feasibility of the spherical 2.5-D modeling scheme.  相似文献   

8.
Offset-dependent characteristics of seismic scattering are useful for characterizing fractured reservoirs. We use two models that have different background medium properties and different azimuthal AVO responses to study elastic wave propagation and scattering in gas-saturated, heterogeneously fractured reservoirs. Heterogeneous fracture density distributions are built through stochastic modelling. Synthetic seismograms are generated by 3-D finite difference modelling, and waveforms along crack-normal and strike directions are considered in this paper. The multiple signal classification (MUSIC) frequency estimator is used in waveform estimation to provide frequency-domain attributes related to seismic wave scattering by fracture heterogeneity. Our results indicate that the strength of the scattering field is a function of the background medium. The strength also increases with increasing fracture scatterer density and with decreasing correlation length of spatial variations of fracture density. The scattering field is weak at the top of the fractured reservoir. The first-order results are dominated by velocity anisotropy of the mean fracture density field. However, the base of the fractured reservoir corresponds to a strong scattering field on which fracture heterogeneity has a larger effect and is characterized by the loss of coherence.  相似文献   

9.
We use teleseismic three-component digital data from the Trabzon, Turkey broadband seismic station TBZ to model the crustal structure by the receiver function method. The station is located at a structural transition from continental northeastern Anatolia to the oceanic Black Sea basin. Rocks in the region are of volcanic origin covered by young sediments. By forward modelling the radial receiver functions, we construct 1-D crustal shear velocity models that include a lower crustal low-velocity zone, indicating a partial melt mechanism which may be the source of surfacing magmatic rocks and regional volcanism. Within the top 5 km, velocities increase sharply from about 1.5 to 3.5 km s−1. Such near-surface low velocities are caused by sedimentation, extending from the Black Sea basin. Velocities at around 20 km depth have mantle-like values (about 4.25 km s−1 ), which easily correlate to magmatic rocks cropping out on the surface. At 25 km depth there is a thin low-velocity layer of about 4.0 km s−1. The average Moho velocity is about 4.6 km s−1, and its depth changes from 32 to 40 km. Arrivals on the tangential components indicate that the Moho discontinuity dips approximately southwards, in agreement with the crustal thickening to the south. We searched for the solution of receiver functions around the regional surface wave group velocity inversion results, which helped alleviate the multiple solution problem frequently encountered in receiver function modelling.
Station TBZ is a recently deployed broadband seismic station, and the aim of this study is to report on the analysis of new receiver function data. The analysis of new data in such a structurally complex region provides constraining starting models for future structural studies in the region.  相似文献   

10.
Summary. High-frequency reflection and refraction seismograms for laterally variable multi-layered elastic media are computed by using the frequency domain elastic Kirchhoff–Helmholtz (KH) theory of Frazer and Sen. Both source and receiver wavefields are expanded in series of generalized rays and then elastic (KH) theory is applied to determine the coupling between each source ray and each receiver ray at each interface. The motion at the receiver is given as a series of integrals, one for each generalized ray. We use geometrical optics and plane wave reflection and transmission coefficients for rapid evaluation of the integrand. When the source or the receiver ray field has caustics on the surface of integration geometrical ray theory breaks down and this gives rise to singularities in the KH integrand. We repair this using methods suggested by Frazer and Sen.
Examples of reflection seismograms for 2-D structures computed by elastic KH theory are shown. Those for a vertical fault scarp structure are compared with the seismograms obtained by physical modelling. Then OBS data obtained from the mid-America trench offshore Guatemala area are analysed by computing KH synthetics for a velocity model that has been proposed for that area. Our analysis indicates the existence of a small low-velocity zone off the trench axis.
No head wave arrivals are obtained in our KH synthetics since we do not consider multiple interactions of a ray with an interface. The nearly discontinuous behaviour of elastic R/T coefficients near the critical angle causes small spurious phases which arrive later than the correct arrivals.  相似文献   

11.
New techniques for improving both the computational and imaging performance of the three-dimensional (3-D) electromagnetic inverse problem are presented. A non-linear conjugate gradient algorithm is the framework of the inversion scheme. Full wave equation modelling for controlled sources is utilized for data simulation along with an efficient gradient computation approach for the model update. Improving the modelling efficiency of the 3-D finite difference (FD) method involves the separation of the potentially large modelling mesh, defining the set of model parameters, from the computational FD meshes used for field simulation. Grid spacings and thus overall grid sizes can be reduced and optimized according to source frequencies and source–receiver offsets of a given input data set. Further computational efficiency is obtained by combining different levels of parallelization. While the parallel scheme allows for an arbitrarily large number of parallel tasks, the relative amount of message passing is kept constant. Image enhancement is achieved by model parameter transformation functions, which enforce bounded conductivity parameters and thus prevent parameter overshoots. Further, a remedy for treating distorted data within the inversion process is presented. Data distortions simulated here include positioning errors and a highly conductive overburden, hiding the desired target signal. The methods are demonstrated using both synthetic and field data.  相似文献   

12.
In this study, we propose a new numerical method, named as Traction Image method, to accurately and efficiently implement the traction-free boundary conditions in finite difference simulation in the presence of surface topography. In this algorithm, the computational domain is discretized by boundary-conforming grids, in which the irregular surface is transformed into a 'flat' surface in computational space. Thus, the artefact of staircase approximation to arbitrarily irregular surface can be avoided. Such boundary-conforming gridding is equivalent to a curvilinear coordinate system, in which the first-order partial differential velocity-stress equations are numerically updated by an optimized high-order non-staggered finite difference scheme, that is, DRP/opt MacCormack scheme. To satisfy the free surface boundary conditions, we extend the Stress Image method for planar surface to Traction Image method for arbitrarily irregular surface by antisymmetrically setting the values of normal traction on the grid points above the free surface. This Traction Image method can be efficiently implemented. To validate this new method, we perform numerical tests to several complex models by comparing our results with those computed by other independent accurate methods. Although some of the testing examples have extremely sloped topography, all tested results show an excellent agreement between our results and those from the reference solutions, confirming the validity of our method for modelling seismic waves in the heterogeneous media with arbitrary shape topography. Numerical tests also demonstrate the efficiency of this method. We find about 10 grid points per shortest wavelength is enough to maintain the global accuracy of the simulation. Although the current study is for 2-D P-SV problem, it can be easily extended to 3-D problem.  相似文献   

13.
Summary. We develop a méthod of reconstructing the elastic paraméters as functions of depth, for a horizontally stratified, isotropic elastic half-space. Unlike previous schemes, which have been able to retrieve the shear wave speed and density from SH seismograms slant stacked at two angles, our méthod makes use of P - SV data at a single stacking paraméter to obtain all three elastic constants. The data required are the elements of the full reflection matrix at the surface, corresponding to measurements of two separate components of the response to two independent sources, one explosive, the other generating shear waves.
In developing this inverse scheme fundamental differences emerge between the acoustic or SH problem, and the coupled P - SV case, the most important being in the nature of the interfacial scattering matrix. We show that it is not possible to make use of the downward reflection data for an interface to determine directly the remaining reflection and transmission coefficients, but that the scattering data may be completed by applying a simple iterative procedure at each interface.
We show the result of applying our inverse scheme to seismograms generated for a six-layered model, including a low-velocity layer. We are able to reconstruct both wave speeds and the density as functions of depth, all quantities being in close agreement with the original model.  相似文献   

14.
理论计算了冰层的声波反射系数,分析了平面冰层覆盖下水中声传播损失特性。将冰层视作平面覆盖层,建立了"空气-冰层-水"结构的冰层反射物理模型,结合冰中的物理声学参数,得到冰层反射系数;利用Bellhop海洋声学传播模型得到冰层覆盖下声场的传播损失,对比分析了传播损失与声波频率、声源深度的关系;结合冰层反射系数计算结果,解释了冰下信道具有频率选择性的原因。结果表明,冰层覆盖下声场传播具有明显的频率选择性,这种频率选择性是由声波频率和冰层厚度共同决定的。  相似文献   

15.
Simulation of SH- and P-SV-wave propagation in fault zones   总被引：3，自引：0，他引：3  
Seismic fault-zone (FZ) trapped waves provide a potentially high-resolution means for investigating FZ and earthquake properties. Seismic waves emitted within and travelling along low-velocity FZ layers may propagate many kilometres within the low-velocity structure associated with the fault. Waveform observation of FZ trapped waves can be modelled in terms of FZ layer velocities, thicknesses and attenuation coefficients. This can greatly improve the resolution of imaged FZ structure and microearthquake locations. At present, broad-band theoretical seismograms are restricted to plane-parallel layers of uniform properties. However, it is not clear how realistic these models are compared with actual fault structures which could, for example, flare outwards near the surface, have irregular boundaries, interior heterogeneities, etc. To address these interpretational uncertainties, we perform finite-difference simulations for irregular FZ geometries and non-uniform material properties within the layers. The accuracy of the numerical solutions are verified by comparison with the analytical solution of Ben-Zion & Aki (1990) for plane-parallel structures. Our main findings are: (1) FZs can widen at the ctustal surface only slightly modifying the trapped waves; (2) velocity variations with depth destroy trapped wave propagation at all wavelengths; (3) FZ trapped waves can be obscured by the presence of a low-velocity surface layer; (4) models with short-scale random structures suggest that trapped waves average out irregular FZ geometries, and hence can be effectively modelled by average-property plane-layered media for the observed range of wavelengths.  相似文献   

16.
2-D full-waveform inversion of double-couple earthquake sources is implemented. Temporally and spatially extended sources are represented by superposition of double-couples. The source parameters solved for are the spatial location, origin time, amplitude and orientation of each double-couple. The velocity and density distribution and source time function are assumed to be known a priori but may be arbitrarily complicated. The non-linear inverse problem is solved by iterative linear approximation. The Jacobian matrix elements for source depth and rupture angle are computed by wavefield extrapolation forward in time, while those for origin time and amplitude are computed analytically. A smoothing technique that results in faster convergence and avoids local minima associated with cycle skipping is applied at each iteration. A spatial sampling interval, between discrete sources, of one-quarter wavelength of the dominant shear wave is optimal for inversion if high uniqueness of the result is desired. The presence of a fault is inferred from the spatial continuity of the rupture solution, rather than being imposed a priori. The method is illustrated by successful application to three synthetic source models: a single double-couple, a single extended rupture and a double extended rupture. The resolutions of the source depth and origin time are higher, and their posterior covariances are lower than those of the amplitude and rupture angle at each source point. Source depth, origin time and amplitude are primarily determined by the data; the rupture angle is more strongly influenced by the a priori information.  相似文献   

17.
Summary. Seismic investigations using shear-wave and converted wave techniques show that very often reflected PS - and SS -waves have anomalous polarizations ( accessory components ). This phenomenon cannot be explained in terms of isotropic models with dipping boundaries. Computations of synthetic seismograms of reflected PS - and SS -waves were made for different models of transversely isotropic media with dipping anisotropic symmetry axes not normal to the boundaries. Synthetic seismograms were computed by ray techniques using an optimization algorithm to construct all rays arriving at a given receiver. These computations indicate that accessory components arise when the medium above the boundary is anisotropic, where they are caused by the constructive interference of qSV - and qSH -waves. If a low-velocity layer is present, displacement vectors of both waves have horizontal projections which are approximately orthogonal. The algorithm for wave separation is presented and some results of its use are given.  相似文献   

18.
I present a 2-D numerical-modelling algorithm based on a first-order velocity-stress hyperbolic system and a non-rectangular-grid finite-difference operator. In this method the velocity and stress are defined at different nodes for a staggered grid. The scheme uses non-orthogonal grids, thereby surface topography and curved interfaces can be easily modelled in the seismic-wave-propagation stimulation. The free-surface conditions of complex geometry are achieved by using integral equilibrium equations on the surface, and the stability of the free-surface conditions is improved by introducing local filter modification. The method incorporates desirable qualities of the finite-element method and the staggered-grid finite-difference scheme, which is of high accuracy and low computational cost.  相似文献   

19.
Elastic scattered waves from a continuous and heterogeneous layer   总被引：3，自引：0，他引：3  
Elastic scattering from a continuous and laterally unbounded heterogeneous layer has been formulated using the Born approximation. A general solution of the scattered wave equation for the above-stated medium has been given in terms of a Fourier integral over plane waves. Far-field asymptotic expressions for weak elastic scattering by a finite, continuous and inhomogeneous layer have been presented which agree with earlier results. For perturbations of the two elastic parameters and the density having the same form of spatial variation, the spectrum of plane waves scattered from a heterogeneous layer is expressed as a product of an 'elastic scattering factor'and a 'distribution factor'. As in earlier results for small-scale heterogeneity, the scattering pattern depends on various combinations of perturbations of elastic parameters and density. In order to show the general characteristics of the elastic wave scattering, some scattering patterns have been given.  相似文献   

20.
Summary. The computational effectiveness of travel-time inversion methods depends on the parameterization of a 3-D velocity structure. We divide a region of interest into a few layers and represent the perturbation of wave slowness in each layer by a series of Chebyshev polynomials. Then a relatively complex velocity structure can be dcscribed by a small set of parameters that can be accurately evaluated by a linearized inversion of travel-time residuals. This method has been applied to artificial and real data at small epicentral distances and in the teleseismic distance range. The corresponding matrix equations were solved using singular value decomposition. The results suggest that the method combines resolution with computational convenience.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号